A gun control group backed by New York Mayor Michael Bloomberg plans a new television advertising campaign this week in a $12 million effort to sway senators’ votes on legislation headed to the floor next month.

But National Rifle Association CEO Wayne LaPierre said the wealthy Bloomberg “can’t spend enough of his $27 billion to try to impose his will on the American public.”

Mayors Against Illegal Guns hopes to be a counterweight to the NRA in the weeks leading up to Senate action on legislation that would require more background checks for gun buyers and an amendment that would ban some assault weapons, Bloomberg said Sunday on NBC’s “Meet the Press.” He and LaPierre appeared in separate segments of the program.

Bloomberg said his group’s ads will appear in 10 states. The mayor earlier told The New York Times that it would be a 13-state effort directed at both Republicans and Democrats.

Bloomberg cited opinion polls that he said showed strong support, even among gun owners, for extending background checks to purchases at gun shows or other venues. An estimated 40 percent of gun purchases occur in private sales. Gun stores are already required to conduct such checks of buyers.

“If 90 percent of the public wants something and their representatives vote against that, common sense is they are going to have a price to pay for that,” Bloomberg said. “The public is going to eventually wake up and say, ‘I want to put in office somebody that will do the things that I think are necessary for this country.’ I don’t think there’s ever been an issue where the public has spoken so clearly where Congress hasn’t eventually understood and done the right thing.”

While Bloomberg sounded optimistic about winning a Senate vote on expanded background checks after the Senate returns April 8 from its current recess, he hedged on the outcome of efforts to ban future sales of some military-style weapons. Majority Leader Harry Reid, D-Nev., has said an assault weapons proposal by Sen. Dianne Feinstein, D-Calif., has no more than 40 supporters.

Reid has said he will bring to the floor a package including background check, gun-trafficking and school safety provisions.

LaPierre called universal or expanded background checks a “dishonest premise. Criminals are not going to be checked. They’re not going to do this.”

He also doubted that universal checks would overcome the current system’s inconsistent access to the records of mentally incompetent people who should be denied weapons.

The current background check system, LaPierre said, “is a speed bump for the law-abiding and does nothing to anybody else.”

LaPierre restated the NRA position that the federal government needs to improve the background check system and its enforcement of current gun laws.

“We are working on a bill right now that will hopefully, at least, get the records of those adjudicated mentally incompetent and dangerous into the check system that applies on dealers,” LaPierre said. “We’re working on laws to beef up the penalties on straw purchases and illegal trafficking, which we want prosecuted.”